LEAP review 1

Solve the following Equations

100

2x+5=18

x=6.5

200

3/4 + y = 1.25

y = 0.5

300

7(x+1)-4=5x+2(4+x)

No solutions

400

2k+16=2k+16

All real numbers; infinite solutions

500

2x /3   +   5x /6  +  x/4  = 42

x=24

Solve the following Inequalities

100

x + 9 < 21

x < 12

200

-6x - 5 < 13

x > -3

300

3x + 2 > 6x - 4

x < 2

400

x + 3(x - 2) > 2x - 4

x > 1

500

(x+1)/2 < (x+2)/4 + (x+4)/6

x < 8

Solve the followingsystems

100

4x-y=3

x-3y=-13

(2,5)

200

8x-2y=24

4x-y=12

(3,0)

300

-x+2y=4

2x+y=7

(2,3)

400

y=2x-5

x=1-y

(2,-1)

500

y=3/4x+15

y=6/8x+5

No solutions, parallel lines

Identify the following as Rational or irrational

100

0.125 and 5/6

Rational

200

sqrt(4)

sqrt(18)

Rational

Irrational

300

𝝅

irrational

400

0.12112111211112111112...

irrational, no specific part of the number ever repeats exactly as before

500

7*𝝅 

Irrational, product of rational and irrational is always irrational (except if the rational number is 0)

Literal Equations

100

4x-y=-23; y

4x=-23+y

4x+23=y

y=4x+23

200

-9x + 6y = 12; y

6y = 12+9x

y = (12+9x)/6

y = 2 + 3/2 x

y = 3/2 x + 2 (Slope intercept form)

300

V=bh ; h

V/b=bh/b

V/b = h

h= V/b

400

P=2(L+W); W

P/2 = L + W

P/2 - L = W

W = P/2 - L

or could distribute 2 to L+W then move and simplify terms as follows:

P=2L+2W

P-2L=2W

(P-2L)/2=W

P/2 - L = W

W= P/2 - L

500

A=𝝅 r² ; r

A/𝝅 = r²

sqrt(A/𝝅)=r

r= sqrt(A/𝝅 )